Responsible production policies with substitution and carbon emissions trading

The green product produced by the green technology can be used as a substitute for the traditional product produced by the standard technology, but not vice versa. Three models are considered. The first model concerns with product substitution only and serves as a benchmark model for the next two models, the carbon emission allowance model and the carbon emission trading model. The second model extends the product substitution model by imposing an upper limit on the total carbon emission allowance for each firm. The third model extends the second model to cater for carbon emission trading. For the carbon emission allowance model, analytical result shows that the optimal production quantity of any product depends on both its total carbon emission allowance quota and its unit carbon emission profit, and the effect of substitution improves the service level, the expected profit of the manufacturer, and the green of product mix. For the carbon emission trading model, analytical result shows that whenever the production quantity of any product is optimal, the marginal profit of production (i.e. the additional profit obtained by producing an extra item) should be equal to the unit price of carbon emission trading within the market. Moreover, the optimal policy of either model reduces the total amount of carbon emission, thus producing less pollution to the environment. Lastly, the optimal profits obtained by using the carbon emission trading model are larger than the corresponding optimal profits obtained by using the carbon emission allowance model.